Organizing for Action – formerly Obama for America – has promised not to accept donations from corporations or lobbying groups. Photograph: Kristoffer Tripplaar/EPA

Barack Obama is coming under mounting fire over the post-election network he has set up across the country to provide popular backing for his second-term agenda, with advocacy groups warning it could spawn a new generation of political fundraising activities that would be a corrupting influence on Washington.

Political finance reformers have expressed alarm at the rapid growth of Organizing for Action, OFA, the campaigning network that builds on the huge success of Obama's grassroots efforts during last year's presidential election. The network exploits the vast database of emails and other information on millions of American voters who have supported Obama in the past, backed up by state-of-the-art digital tools and social media outreach that was developed in the run up to the November ballot.

OFA on Thursday held a series of closed-door sessions on the second of a two-day conference in Washington designed to take the organisation to prominent and wealthy liberal Americans. The event was billed as a "founders summit" and was kicked off on Wednesday with a glitzy dinner attended by Obama, who, in a short speech, repeated his now familiar refrain: "You can't change Washington from the inside."

In the speech, Obama lamented that after his first White House victory in 2008, he and his coterie of advisers had failed to find a way of harnessing the extraordinary energy that was unleashed during that presidential campaign. Now in his second term, the president is trying – with added determination – to achieve the goal of using his vast database of emails and social media connections through Facebook and Twitter to strengthen his standing on Capitol Hill.

The tool is being seen within the Obama inner circle as a crucial advantage as he enters a fresh round of clashes with Republicans – this time over sequestration, gun reform, immigration and climate change. But it has prompted a chorus of criticism from public watchdogs who see it as setting a potentially dangerous precedent.

"We think this is a mistake, and that President Obama should shut it down," said Fred Wertheimer of the campaign for finance reformers Democracy 21. "If this is legitimised by Obama, even though we don't think it can be legitimised, then you will see these entities popping up all over Capitol Hill."

OFA has tried to assuage some of the sharpest criticism by promising not to accept donations from corporations, lobbying groups or foreign interests. It has also promised to disclose the identity of all donors who give more than $250.

But the watchdogs are still troubled by the fact that because it is constituted as a "non-partisan" 501(c)3 group, it can collect unlimited donations from individuals and is legally under no obligation to disclose any information. "If this new kind of vehicle catches on, it will open the door for all kinds of abuses above and beyond what OFA itself is doing," Wertheimer said.

He accused OFA of setting a terrible example to other politicians who may be less scrupulous in setting themselves standards: "You could have a member of Congress setting up an entity like this, and accepting money from China or a foreign communications corporation or an American company, and none of that money would have to be disclosed."

Mary Boyle of Common Cause said that there were also questions about transparency. The organisers have stressed that it will provide no access for cash, but yet it still plans to hold quarterly board meetings held in Washington, with Obama attending, to which top donors would be invited.

"We have no problems with OFA utilising their grassroots organisation to help the president achieve his agenda, but if they are going to continue operating in this way they should impose the same caps on contributions as political parties do. Given Obama's profile, there's nothing to stop OFA running on small donations alone. It doesn't need to draw big donations that can only lead to access and return of favours," Boyle said.

OFA has been formed directly out of the 2012 presidential re-election campaign that bore the same acronym but different title: Obama for America. Apart from the name change, everything else is the same: the senior executive team led by Jim Messina and Jon Carson, the headquarters in Chicago, down to the website URL – barackobama.com.

Messina has insisted that OFA will keep away from "electoral politics". But in its opening activities it has focused on precisely those core policy areas that are currently pitting the president against the prevailing Republican group in Congress.

On Thursday, OFA sent an email to its more than 1 million signatories that encouraged them to agitate for the passage of a universal background check on all gun sales. "Let's get this done. We're going to need to keep the pressure on our elected officials by raising our voices, so add your name and say that you're not going to let Congress drag their heels on this one."

An earlier OFA email on the federal budget cuts urged supporters to lobby their local Congress member through Twitter. The email linked users to the Twitter website and composed a tweet for them that said: "I'm standing with you to end the sequester. Keep fighting to stop #CutsWeCantAfford".

On the other end of the scale, OFA is also going after high-profile and wealthy participants prepared to open their ample cheque books. Wednesday's dinner had 75 guests for "founding members", including Eric Schmidt of Google, with places costing a suggested $500 each.

According to the Washington Post, Messina and Carson, OFA's chairman and director respectively, have been suggesting that top donors aim to gather $500,000 to give the new organisation.